PRP Records

Probable Primes Top 10000

(225451 PRPs in the top)


What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!


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1-250   251-500   501-750   751-1000   1001-1250   1251-1500   1501-1750   1751-2000   
2001-2250   2251-2500   2501-2750   2751-3000   3001-3250   3251-3500   3501-3750   3751-4000   
4001-4250   4251-4500   4501-4750   4751-5000   5001-5250   5251-5500   5501-5750   5751-6000   
6001-6250   6251-6500   6501-6750   6751-7000   7001-7250   7251-7500   7501-7750   7751-8000   
8001-8250   8251-8500   8501-8750   8751-9000   9001-9250   9251-9500   9501-9750   9751-10000   


Rank Probable prime Digits (> 30000) Who ? When ?
900120^42973-558355910Enzo Doria03/2013
90024*10^55906+2155907Robert Price08/2016
90032^185713-11155906Lelio R Paula03/2011
900413^50174+8855891Lelio R Paula01/2013
900514569^6846+6846^1456955879Hans Havermann08/2016
9006Pell-LucasQ(145969)/255874Eric W. Weisstein08/2006
90073^117087-8055865Lelio R Paula10/2012
9008(7*10^55851-43)/955851Robert Price10/2014
90092^185519-16955847Lelio R Paula03/2011
90107^66074+1055840Lelio R Paula10/2012
9011(19*10^55833-49)/355834Robert Price02/2017
9012(2*10^55834-59)/355834Robert Price05/2017
90132^185463-423755830Yves Minet08/2018
901412^51732+555829Lelio R Paula01/2013
90153*2^185429+755821Lelio R Paula03/2014
9016(60^31393+1)/6155820Paul Bourdelais08/2017
9017(9787*2^185420-1)/38155819Lelio R Paula04/2015
901814427^7396+7396^1442755819Hans Havermann08/2016
901910^55811+2155812Robert Price01/2011
902010^55811-7410355811Patrick De Geest12/2012
902111^53591-153055810Enzo Doria11/2012
9022(5^79841-5^39921+1)/1533415955800Lelio R Paula09/2017
90232^185355-214555798Lelio R Paula03/2011
902414531^6912+6912^1453155794Hans Havermann07/2016
90252^185327-161555789Lelio R Paula03/2011
90262^185280-1277955775Enzo Doria10/2012
902715504^3955+3955^1550455771Hans Havermann07/2016
9028(2*10^55762-59)/355762Robert Price05/2017
90295^79770-4455757Lelio R Paula10/2012
903018^44416-8555755Lelio R Paula02/2013
90312^185208-45999555754Enzo Doria06/2015
90322^185200+118555751Lelio R Paula03/2011
9033(536*10^55748-23)/955750Robert Price11/2017
90347^65964+6^(65964-1)55747Robert Price03/2016
90352^185151-23715755737Gary Barnes09/2009
9036110017^11055-10255734Enzo Doria07/2012
903714754^5987+5987^1475455729Hans Havermann07/2016
903812591^13592-13592^1259155729Norbert Schneider07/2018
903940090!3-955711Robert Price09/2014
90409*10^55707+8955708Robert Price11/2016
90412^185023-225755698Yves Minet06/2009
904218628^977+977^1862855696Anatoly F. Selevich01/2007
90432^185006-9355693Lelio R Paula03/2011
90442^185003-251555692Yves Minet07/2014
90452^184992-7855755689Jorge Menendez02/2018
90463*10^55679+3755680Robert Price10/2017
90476^71524-1955657Lelio R Paula10/2012
90482^184872-219555653Yves Minet08/2013
9049507^20572+20572^50755648Norbert Schneider06/2016
9050(86*10^55645-311)/955646Robert Price10/2017
9051134^26151-13355626Norbert Schneider03/2015
905215340^4221+4221^1534055614Hans Havermann07/2016
905327743!2+255612Robert Price01/2013
905420^42744+8155612Lelio R Paula02/2013
905514609^6406+6406^1460955611Hans Havermann07/2016
90562^184724-11288355608Enzo Doria06/2014
905713507^13074+13074^1350755601Hans Havermann07/2016
90582^184689+12955597Lelio R Paula03/2011
9059(9179*2^184672-1)/19355594Lelio R Paula03/2015
9060(22*10^55592-19)/355593Robert Price02/2017
9061Phi(59984,89)55582Enzo Doria05/2012
906211^53368+1655578Lelio R Paula01/2013
906320^42717-192355577Enzo Doria03/2013
9064117^26870+26870^11755573Serge Batalov05/2014
906512^51488+5555565Lelio R Paula01/2013
9066(44*10^55558-17)/955559Robert Price06/2015
9067(2*10^55559-23)/355559Robert Price09/2017
906810^55555+3285755556Patrick De Geest06/2010
906910^55555-13672155555Patrick De Geest06/2010
9070(11*2^184541-1)/35155551Lelio R Paula01/2014
907120^42696-204355549Enzo Doria03/2013
9072(35*10^55547-737)/955548Robert Price11/2017
9073(2*10^55544+1)/355544Serge Batalov06/2009
9074(-lucasV(1,2,369056)+2)/(3*89*109*457)55542Mike Oakes04/2017
90755003^15013-16055537Enzo Doria07/2012
907639^34896-255522Lelio R Paula08/2013
9077(6^71345-61)/555517Lelio R Paula05/2014
90782^184407-301955513Yves Minet10/2014
9079(43*10^55512-61)/955513Robert Price06/2015
908020^42667-84355512Enzo Doria03/2013
9081133^26134-13255505Norbert Schneider03/2015
9082(31*2^184378-1)/71155502Lelio R Paula01/2014
90839*7^65667-455497Lelio R Paula09/2014
90842^184342-17355493Lelio R Paula03/2011
908515^47182+9255491Lelio R Paula02/2013
90865^79378+655483Lelio R Paula10/2012
9087581^20068+20068^58155472Norbert Schneider06/2016
9088(2^184232+1)/25755457Donovan Johnson03/2005
908918^44177-141555455Enzo Doria03/2013
90902^184203-279786755451Enzo Doria04/2016
90912^184189+1755447Lelio R Paula03/2011
90922^184183+2612355445Yves Minet01/2010
9093Phi(77077,10)55441Ray Chandler05/2009
90942^184141-11325155432Enzo Doria07/2014
90952^184093-50461355418Gary Barnes09/2009
9096(lucasV(1,2,368167)+2)/(11*1103*1307*5647)55404Mike Oakes04/2017
90972^184044-11126955403Enzo Doria05/2014
909814051^8766+8766^1405155401Hans Havermann07/2016
909998^27819+27819^9855394Serge Batalov05/2014
9100(178*10^55390-7)/955392Robert Price08/2017
910158046^9+9^5804655390Andrey Kulsha02/2004
91027^65536+2*59232-255385Jiahao He07/2017
91032^183980+7524155384Enzo Doria04/2016
910410^55372+3755373Robert Price01/2011
910510^55372-4996755372Patrick De Geest12/2012
9106(13*10^55367+17)/355368Robert Price06/2015
91072*6^71150+755366Lelio R Paula09/2014
910819^43296-6255365Lelio R Paula02/2013
910919^43295+1055364Lelio R Paula02/2013
9110(29*10^55362-11)/955363Robert Price04/2015
9111(37*10^55359+53)/955360Robert Price05/2015
911219^43283+7255349Lelio R Paula02/2013
91132^183800-6555330Lelio R Paula03/2011
911421001^12801-11055329Enzo Doria07/2012
911533^36433-32^3643355325Robert Price04/2012
9116(17*2^183729+1)/14555308Lelio R Paula07/2012
91179^57952+8^(57952-1)55301Robert Price03/2016
911814872^5229+5229^1487255301Hans Havermann08/2016
911961^30972-255296Lelio R Paula08/2013
91202^183671-11253755291Enzo Doria06/2014
9121(2^183687+7)/49793974555287Lelio R Paula02/2012
91223^115873+5655286Lelio R Paula10/2012
912313^49629-8455284Lelio R Paula01/2013
91242^183632-555279Henri Lifchitz08/2005
912513981^8988+8988^1398155277Hans Havermann07/2016
912610688^13719-13719^1068855273Norbert Schneider09/2018
9127(5*2^183585+1)/1355265Lelio R Paula07/2012
91282^183576+17155262Lelio R Paula03/2011
912913^49604+8255257Lelio R Paula01/2013
9130(11*10^55254+1)/355255Erik Branger03/2014
913112609^13474-13474^1260955253Norbert Schneider05/2018
91323^115802-2655252Lelio R Paula10/2012
91332^183534-364555250Lelio R Paula01/2011
9134(15*2^183533-1)/11355249Lelio R Paula01/2014
91355^79032-1376655241Enzo Doria02/2013
91368*3^115759-755232Lelio R Paula03/2014
91376^70974-13755229Lelio R Paula10/2012
91382^183466+52428755229Paul Underwood08/2018
91392^183446-11307355223Enzo Doria07/2014
91402^183441+57729457555222Lelio R Paula03/2013
91415^79000-655219Lelio R Paula10/2012
91422^183413-90155213Yves Minet01/2012
914319^43168-5055202Lelio R Paula02/2013
91442^183340+1968355191Lelio R Paula02/2012
91456^70923+3555189Lelio R Paula10/2012
91462^183317-403555184Lelio R Paula01/2011
91472^183284-1555174Lelio R Paula03/2011
91482^183255+14955166Lelio R Paula02/2011
91494*10^55165+8755166Robert Price05/2016
9150(3^115574+4)/6303755139Lelio R Paula03/2012
91512^183165-11233355139Enzo Doria06/2014
9152(109^27061-1)/10855133Richard Fischer09/2017
91532^183142+85555132Lelio R Paula01/2011
9154(49*10^55129+383)/955130Robert Price04/2017
91552^183019+25525555095Lelio R Paula01/2011
9156(10^55084-19)/955084Robert Price10/2017
91573*10^55077+755078Erik Branger11/2013
9158(62*10^55075-71)/955076Robert Price09/2015
915927499!2-3255070Robert Price10/2015
916015307^3958+3958^1530755067Hans Havermann08/2016
916170^29836-6955051Norbert Schneider10/2012
916218^43854-8355049Lelio R Paula02/2013
91637^65126+5855038Lelio R Paula10/2012
91642^182827-161555037Lelio R Paula11/2009
91657*10^55030-955031Dmitry Domanov11/2010
91669027^13912-13912^902755030Norbert Schneider08/2018
91672^182768-405555019Yves Minet02/2018
91686^70702+2355017Lelio R Paula10/2012
9169(23*2^182753+1)/15155014Lelio R Paula07/2012
91702^182743-161555012Lelio R Paula11/2009
9171(24737*2^182736+1)/39955011Lelio R Paula05/2014
91723^115280-956855003Enzo Doria02/2013
91732^182656-1284954985Enzo Doria10/2012
917412791^13388-13388^1279154984Norbert Schneider03/2018
91759*19^42995+1654981Curtis Bright05/2015
91762^182627+2842554977Lelio R Paula11/2009
91772^182597-11305354968Enzo Doria07/2014
9178(3^115213+2)/3090672554964Lelio R Paula03/2012
91792^182581-197554963Yves Minet09/2012
9180(2*10^54960-179)/354960Robert Price11/2017
918127449!!-1654959Robert Price06/2015
9182(22*10^54958-73)/354959Robert Price09/2017
91834^91283-3^9128354958Jean-Louis Charton01/2004
91842^182565+10754958Lelio R Paula11/2009
91852^182560+205354957Lelio R Paula12/2010
91862^182451-18245154924Henri Lifchitz10/2004
91872^182444+8154922Henri Lifchitz10/2005
91882^182433+7410554918Enzo Doria04/2016
918920^42206-524354912Enzo Doria03/2013
91902^182394+8554907Lelio R Paula02/2011
91912^182374-11228754901Enzo Doria06/2014
9193(47^32833-33^32833)/1454899Serge Batalov12/2016
919210188^13697-13697^1018854899Norbert Schneider09/2018
91942^182363-11316754897Enzo Doria07/2014
91952^182359-11222154896Enzo Doria06/2014
9196(F(1905)^139-F(1904)^139)/F(1903)54893Wayne Halsdorf05/2010
9197(17*2^182274+1)/146754869Lelio R Paula01/2012
919818^43698-554853Lelio R Paula02/2013
91992^182209-189354851Yves Minet09/2012
92002^182194-344354846Yves Minet12/2016
920115023^4468+4468^1502354836Hans Havermann08/2016
92022^182135+9014354829Yves Minet10/2010
92032^182119+7433354824Enzo Doria04/2016
920414289^6860+6860^1428954818Hans Havermann08/2016
92053^114892-114892^354818Norbert Schneider03/2017
92062^182070-4735554809Lelio R Paula01/2011
92073^114869+7654807Lelio R Paula10/2012
92088^60681-60681^854801Norbert Schneider12/2016
92091897^16710+16710^189754777Serge Batalov05/2014
9210Phi(61868,59)54776Enzo Doria04/2012
9211113^26679+254775Lelio R Paula05/2013
92123^114789-7454769Lelio R Paula10/2012
921315^46567+9854768Lelio R Paula02/2013
9214(2*10^54767-71)/354767Robert Price01/2017
9215(298*10^54765-7)/354767Robert Price06/2017
9216(21*2^181931-1)/16999754763Lelio R Paula01/2014
92182^181913+2954762Henri Lifchitz06/2005
9217(31*10^54761-121)/954762Robert Price06/2016
92192^181887+18954754Lelio R Paula02/2011
92202^181874+181874^2-154750Robert Price04/2014
9221(2^181865+9)/733954743Lelio R Paula02/2012
92225^78314-9254740Lelio R Paula10/2012
9223(163*10^54727-1)/954729Serge Batalov12/2014
922415^46531+7454725Lelio R Paula02/2013
9225277^22400-34854712Enzo Doria07/2012
92266^70302+10154706Lelio R Paula10/2012
92273^114622-1040854689Enzo Doria02/2013
9229(23*2^181674+1)/48954688Lelio R Paula01/2012
92282^181669-155154688Yves Minet08/2012
9230(57352^11491-1)/5735154676Serge Batalov04/2015
9231(31*2^181629-1)/1073472154671Lelio R Paula01/2014
9232(F(1048)^251-F(1047)^251)/F(1046)54668Wayne Halsdorf05/2010
923313^49073+4654665Lelio R Paula01/2013
9234(57042^11491-1)/5704154649Serge Batalov04/2015
923620^42000+7354644Lelio R Paula02/2013
9235(67607*2^181517+1)/165554644Lelio R Paula05/2014
923733*10^54634+754636Robert Price07/2016
923820^41988+6154628Lelio R Paula01/2013
923920^41988-812354628Enzo Doria03/2013
92412^181420+2118154613Yves Minet03/2011
92409854^13675-13675^985454613Norbert Schneider08/2018
9242(19*10^54608+161)/954609Robert Price07/2016
924319^42696-2454598Lelio R Paula02/2013
9244(44*10^54596-503)/954597Robert Price10/2017
9245(74*10^54583+61)/954584Robert Price10/2015
92462^181316-9439554582Lelio R Paula09/2011
924714751^5006+5006^1475154572Hans Havermann08/2016
924814^47609+3954567Lelio R Paula02/2013
924912696^13295-13295^1269654559Norbert Schneider01/2018
9250(2^124979+lucasV(2,-2,124979)+1)/354552Paul Vanderveen12/2017


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: October, 20 2018 23:15 (Time in France)

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